On the Topological Classification of Four-Dimensional Steady Gradient Ricci Solitons with Nonnegative Sectional Curvature

In this paper, we study the topology of steady gradient Ricci solitons with nonnegative sectional curvature. We apply a characterization theorem for the fundamental group of a positively curved steady gradient Ricci soliton that admits a critical point. As an application of the characterization theorem, we give a classification of the topology of complete four-dimensional steady gradient Ricci solitons with nonnegative sectional curvature.